Towser is a Demon Dog living in an unknown world. His owners are Chrestomanci's agent and Prudence. His name is a common dog name (there is even a dog called Towser in The Pinhoe Egg). Towser attacked the Willing Warlock multiple times when he tried to escape from the car and forced him to drive.
Towser is described as "a great pepper coloured brute with white fangs to match the size of the rest of it".